Talk:Diversity index

This page is inconsistent with Simpson's diversity index, but this one is correct. Perhaps the other page should be deleted/merged? 128.42.145.156 (talk) 06:11, 10 November 2009 (UTC)

"Diversity of population" should be "diversity of community" since a population refers to one species - therefore, a measure of species richness cannot be applied to a population and instead must be applied to a community of species. 82.19.72.160 (talk) 17:08, 7 January 2010 (UTC)

Introduction

"A diversity index is a quantitative measure that increases when the number of types into which a set of entities has been classified increases, and obtains its maximum value for a given number of types when all types are represented by the same number of entities"

errr.. what? i think a simpler introduction is needed. --128.250.5.249 (talk) 07:48, 21 August 2012 (UTC)

Definition Shannon-Index

I think the definition is wrong, in my opinion it should be "ln" instead of "log". Maybe someone could check? --93.133.255.155 (talk) 16:54, 10 December 2012 (UTC)

True diversity (The effective number of types)

Why does the definition of qD have the term p_i*p_i^(q-1), when this is simply equal to p_i^q? It seems these two p's may be slightly different, however this is not clear in the text. — Preceding unsigned comment added by Bbeckerman (talk • contribs) 21:51, 23 September 2013 (UTC)

This is to make clear that it is a weighted power mean with exponent q-1 and weights equal to p_i.2600:1702:3190:38A0:59B8:2AD3:9EA8:F2D0 (talk) 18:13, 8 August 2021 (UTC)

Generalized diversity

The article focuses on weighted generalized means, where the generalized mean is restricted to the form $M_{q-1}=\left(\sum _{i}w_{i}p_{i}^{q-1}\right)^{1/(q-1)}$ for any q≥0, and where the weight w_i is required to be simply p_i. However, for any weighting function w(p) and any strictly monotonic function f(p), there is a more general mean

$M_{w,f}=f^{-1}\left({\frac {\sum _{i}w(p_{i})f(p_{i})}{\sum _{i}w(p_{i})}}\right)=1/D^{w,f}\,.$

That is, one takes the weighted average of the f(p_i) values, where the denominator in the definition of M_w,f normalizes the weights to sum to 1, and then uses the inverse of f to bring that weighted average back to the same space that the p_i values live in. If you have citations to the literature for this general diversity index, would you add them and a discussion to the article? Leegrc (talk) 14:30, 13 February 2015 (UTC)

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Reorganization/Can we remove the Multiple Issues tag?

I just made an edit to reorganize the page by moving the section "Effective number of species or Hill numbers" from the end of the article to the beginning. (Other than that, I didn't change the article except for a few minor things like taking out the word "different" when it was unnecessary, changing "more equal" to "closer", and other wording changes, as well as adding a link to the article on the number one in case some readers don't know that "unity" is another word for "one"). This change was necessary because the article refers to the effective number of species ^qD throughout. It also refers to the parameter q and the generalized mean M_q-1 throughout but did not mention what either one meant the first time they were mentioned. The article made no sense when it was organized this way, so I moved the section defining ^qD and M_q-1 to the beginning. The article now flows much better. I am also wondering if we still need the multiple issues tag. It looks like every issue in the Talk page has been resolved except for the section "Generalized diversity", but that section is just a suggested addition, not an issue with the article. 2600:1702:3190:38A0:59B8:2AD3:9EA8:F2D0 (talk) 18:45, 8 August 2021 (UTC)

I just changed 'unity' to one (1) throughout. Although I'm sure that using 'unity' to mean 'one' is common enough in some fields, I'm a professor in a STEM field and had never encountered it before this article, so it definitely qualifies as jargon that we'd want to replace to make the article more accessible. 2601:152:5001:7CD0:F8FC:6F00:7C8:E979 (talk) 18:09, 7 September 2023 (UTC)